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11.5 Exercise 9

Avg difficulty 2.5

The country of San Lorenzo has grown from two states to three. The house size of the congress has been increased by eight and the seats have been reapportioned to accommodate the new state of Oscuridad. The constitution mandates the use of the Hamilton method of apportionment. Use this information and the following table to answer the questions.

State Population (in hundreds) Original Apportionment Reapportionment
Clara 7,100 39 40
Velasco 9,080 51 50
Oscuridad 1,500 Not Applicable 8
  1. What was the original house size?
  2. What is the new house size?
  3. How is this reapportionment an example of the new-states paradox?

OpenStax Contemporary Mathematics, 11.5 Fairness in Apportionment Methods, exercise 9

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Adapted from Contemporary Mathematics © 2023 Rice University. Licensed under CC BY 4.0. Source: Contemporary Mathematics. Imported at revision fa7c1a1.